Write the expression in simplest form. (2a+b)/(4a^(2)-b^(2))

Recognize the denominator: Recognize the denominator as a difference of squares. The denominator 4a^2 - b^2 can be factored using the difference of squares formula, which is a^2 - b^2 = (a + b)(a - b).Factor the denominator: Factor the denominator. 4a^2 - b^2 = (2a)^2 - b^2 = (2a + b)(2a - b)Simplify the expression: Simplify the expression by canceling out common factors. The numerator (2a + b) has a common factor with one of the factors in the denominator (2a + b). (2a + b) / [(2a + b)(2a - b)] = 1 / (2a - b)Write final simplified expression: Write down the final simplified expression. The expression simplifies to 1 / (2a - b).

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Write the expression in simplest form.
(2a+b)/(4a^(2)-b^(2))

Write the expression in simplest form. $\newline$ $\frac{2 a+b}{4 a^{2}-b^{2}}$

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Algebra 2

Simplify radical expressions involving fractions

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Q. Write the expression in simplest form.

\newline

\frac{2 a+b}{4 a^{2}-b^{2}}

Recognize the denominator: Recognize the denominator as a difference of squares. The denominator $4a^2 - b^2$ can be factored using the difference of squares formula, which is $a^2 - b^2 = (a + b)(a - b)$ .
Factor the denominator: Factor the denominator. $\newline$ $4a^2 - b^2 = (2a)^2 - b^2 = (2a + b)(2a - b)$
Simplify the expression: Simplify the expression by canceling out common factors. $\newline$ The numerator $(2a + b)$ has a common factor with one of the factors in the denominator $(2a + b)$ . $\newline$ $(2a + b) / [(2a + b)(2a - b)] = 1 / (2a - b)$
Write final simplified expression: Write down the final simplified expression. $\newline$ The expression simplifies to $\frac{1}{2a - b}$ .